Add syllabus content for Applied Math Lab, detailing course structure and session topics

Author: Daniel Precioso

syllabus.qmd

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+---
+title: "Applied Math Lab"
+subtitle: "Syllabus (Program Overview)"
+format:
+  html:
+    toc: true
+    number-sections: true
+---
+
+# Program
+
+This course has **10 live in-person sessions**.
+
+## Session 1 — 1D ODEs (SciPy + Streamlit)
+
+Simulate classical one-dimensional ODE models (SIR epidemiological model, spruce budworm population model, Michaelis–Menten enzyme kinetics). Solve ODEs numerically with SciPy in Python, and build/deploy a simple Streamlit web app to explore parameter effects. Groups are assigned and remain for the whole course.
+
+## Session 2 — 2D ODEs (Nonlinear Oscillators)
+
+Explore two-dimensional ODEs via nonlinear oscillatory systems: Van der Pol oscillator and FitzHugh–Nagumo model. Create animations with matplotlib and build interactive Python programs that let users set initial conditions via mouse clicks.
+
+## Session 3 — PDEs via Reaction–Diffusion Systems
+
+Introduce partial differential equations through reaction–diffusion models (Gierer–Meinhardt and Gray–Scott). Implement 1D and 2D Laplacians with NumPy and animate spatiotemporal evolution to study Turing instability and pattern formation.
+
+## Session 4 — Coupled ODEs (Kuramoto Model)
+
+Implement coupled ODEs, focusing on the Kuramoto model. Animate multiple plots simultaneously (e.g., oscillator evolution and a bifurcation diagram).
+
+## Session 5 — Flocking (Vicsek Model)
+
+Simulate flocking behavior using the Vicsek model. Implement interaction rules for “boids” and extend the simulation by treating the mouse as a predator and coding avoidance behavior.
+
+## Session 6 — Networks I (NetworkX Fundamentals)
+
+Introduce NetworkX: build graphs, compute structural metrics (degree distribution, clustering coefficient, centrality), and visualize different network types. Establish foundations for modeling dynamics on networks.
+
+## Session 7 — Networks II (Spreading on Real Networks)
+
+Simulate spreading processes (fake news, epidemics) on real-world networks. Retrieve and process open-source network datasets, and investigate how network structure shapes propagation dynamics.
+
+## Session 8 — Cellular Automata I (1D CA)
+
+Introduce one-dimensional cellular automata as a framework for discrete dynamical systems. Explore deterministic and stochastic CA, and how simple local rules generate complex global behavior.
+
+## Session 9 — Cellular Automata II (Traffic Dynamics)
+
+Apply cellular automata to traffic modeling with the Nagel–Schreckenberg model. Study congestion, flow, and phase transitions by tuning parameters such as vehicle density and maximum speed.
+
+## Session 10 — Final Project Support
+
+Wrap-up and support session for the final project: address remaining questions, clarify concepts, and help groups prepare deliverables.